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Results tagged with descriptive-set-theory
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user 41274
Descriptive Set Theory is the study of definable subsets of Polish spaces, where definable is taken to mean from the Borel or projective hierarchies. Other topics include infinite games and determinacy, definable equivalence relations and Borel reductions between them, Polish groups, and effective descriptive set theory.
9
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Uncountable disjoint closed coverings of $[0,1]$
It is well known that the unit interval $[0,1]$ cannot be decomposed as a countable union of pairwise disjoint closed (nonempty) subsets. See for instance this math.stackexchange question. The proof u …
- 1,688
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votes
1
answer
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Generic sections of non-null sets are non-null
Consider the Cantor space $\mathcal C={}^\omega2$ with the usual product measure, and let $r$ be a random real (over a transitive model $V$ of ZFC). Let $B\subset \mathcal C^V\times\mathcal C^V$ a Bor …
- 1,688
3
votes
1
answer
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Representation of meager sets in Cohen extensions
Let $M$ be a transitive model of ZFC and $c\in {}^\omega2$ a Cohen real over $M$. Let $A$ be a meager Borel subset of $^\omega2$ in $M[c]$. I would like to prove that there exists a meager Borel set $ …
- 1,688
6
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1
answer
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Iteration of random reals
Consider two random reals $x, y$ over a transitive model $V$ of ZFC. More specifically, if $\mathcal C^V={}^\omega2$ is the Cantor space, composing the canonical homeomorphism with the projections $\m …
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